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# A, B, C are three positive numbers. Which is the greatest number

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Retired Moderator
Joined: 22 Aug 2013
Posts: 1428
Location: India
A, B, C are three positive numbers. Which is the greatest number  [#permalink]

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17 Mar 2018, 00:33
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Difficulty:

55% (hard)

Question Stats:

58% (01:30) correct 42% (01:28) wrong based on 47 sessions

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A, B, C are three positive numbers. Which is the greatest number among A, B, C?

(1) A*B > B*C > C*A

(2) 1/C > 1/A > 1/B
Retired Moderator
Joined: 25 Feb 2013
Posts: 1178
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GPA: 3.82
A, B, C are three positive numbers. Which is the greatest number  [#permalink]

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17 Mar 2018, 05:43
1
amanvermagmat wrote:
A, B, C are three positive numbers. Which is the greatest number among A, B, C?

(1) A*B > B*C > C*A

(2) 1/C > 1/A > 1/B

Statement 1: $$A*B > B*C => A>C$$ and $$B*C > C*A => B>A$$

Therefore $$B>A>C$$. Sufficient

Statement 2: $$\frac{1}{C}>\frac{1}{A} =>A>C$$ AND $$\frac{1}{A}>\frac{1}{B} => B>A$$

Therefore $$B>A>C$$. Sufficient

Option D
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Re: A, B, C are three positive numbers. Which is the greatest number  [#permalink]

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20 Mar 2018, 01:22
amanvermagmat wrote:
A, B, C are three positive numbers. Which is the greatest number among A, B, C?

(1) A*B > B*C > C*A

(2) 1/C > 1/A > 1/B

Experts pls advice if i am on correct line of understanding.

for 1. A*B > B*C > C*A

case I :
Considering, A : 3 , B : 2, C : 1

we get, 3/2 , 2/1 , 1/3
1.5, 2, 0.33

case II :
Considering, A : 6 , B : 2, C : 1

we get, 6/2 , 2/1 , 1/6
3 2 0.16

both situations provide a different answer, so how can statement (1) be sufficient in itself??

experts and friends pls revert
Retired Moderator
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: A, B, C are three positive numbers. Which is the greatest number  [#permalink]

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20 Mar 2018, 05:52
GMAT215 wrote:
amanvermagmat wrote:
A, B, C are three positive numbers. Which is the greatest number among A, B, C?

(1) A*B > B*C > C*A

(2) 1/C > 1/A > 1/B

Experts pls advice if i am on correct line of understanding.

for 1. A*B > B*C > C*A

case I :
Considering, A : 3 , B : 2, C : 1

we get, 3/2 , 2/1 , 1/3
1.5, 2, 0.33

case II :
Considering, A : 6 , B : 2, C : 1

we get, 6/2 , 2/1 , 1/6
3 2 0.16

both situations provide a different answer, so how can statement (1) be sufficient in itself??

experts and friends pls revert

Hello

You are dividing, As per the first statement you are supposed to multiply not divide.
Re: A, B, C are three positive numbers. Which is the greatest number   [#permalink] 20 Mar 2018, 05:52
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